The Ike is a known and obvious bottlebeck. It's unclear a rapid transit extension is warranted - depending on the exact alignment and operating plan (e.g. if the extension had BART-style headways and fares in the furthest stretches) perhaps a west extension could be successful, but it's tough to imagine or locate a viable alignment to Oak Brook/Lombard. Getting it to 4-lanes each direction through Oak Park and the Avenues is probably a necessary project, but I fear what the traffic engineers will try to do to the area around Oak Park avenue, which is a surprisingly thriving and dense piece of urbanity (served by a transit stop but no highway access, and the built form and mode choice patterns show it).
Both the I-90 and I-290/88 corridors would probably be most effectively served by a robust express bus network hubbing at Rosemont and Forest Park, respectively, with serious facilities in place to bypass any congestion a la Houston's fully separated entry/exit ramps and HOV lanes. If memory serves, I'm pretty sure the Alternatives Analysis study of the Northwest corridor (I-90) which looked at Blue Line extensions, express bus, local bus, and commuter rail options showed the express bus as far and away the most cost effective at improving accessibility and reducing travel times - but I can't find the doc to be sure so don't quote me on it or present that statement as fact ("I read on the internet that..."). Of course, we know how
that whole study turned out... due to the triumph of politics.
Of the proposed extensions, well, clearly there are political considerations at play. To my eyes, based on travel patterns and regional economics, the "no-brainer" of these 3 is the Orange Line extension, though all have potential merit assuming costs can be kept from ballooning to the stratosphere.
The Brown Line extension to Jefferson Park is probably the only hope for any sort of E-W rapid transit in the city, which is also a marginal project that has good ridership potential but exorbitant cost. Most other crosstown corridors just dont have the trip density to support rail rapid transit, and would be better off just getting serious bus improvements (rush-hour bus-only lanes, signal priority, some use of pre-paid multi-door boarding, etc.).
The other main issue with crosstown corridors is that average trip lengths tend to be very low, between 1.5-3 miles, which is not an optimal range for rapid transit which shines for trip lengths in the 4-8 mile range. At short trip lengths, the bus almost always wins for the simple reason that it has more closely spaced stops that get people to/from destinations with less walking - the station access times at both ends of the trip negate the travel time savings of rail for most people when their overall trip length is short. The Brown extension under Lawrence to Jeff Park potentially works because of the demand generated by O'Hare and surrounding economic activity at Rosemont, Cumberland, etc. in conjunction with the high residential density of the north side - e.g. it serves a relatively high concentration of long trips for which rail would be much more attractive than a very long bus ride, but it's also exorbitantly expensive to build so it's not a no-brainer extension.